2. Cable from modem to Airport, then ethernet cable from airport to imac = works for awhile, but later in evening or next day (computer sleeping) I have to unplug the cable modem off/on for it to work again. Also when other computers in the house are on, they see the airport, that it is online, full bars, but for the internet connection to work, the cable modem must be powered on & off.

Question, do I need to purchase a new airport extreme? Why must I keep turning the modem on/off for my wireless connections to work?

When the imac is directly patched to the modem and if the computer sleeps, there is no need to turn modem on/off. The internet connection remains.

I'll go out on a limb here and guess your AirPort is misconfigured for your network.

In order for the AirPort to share the cable connection it has to be setup as a NAT device (done by selecting the 'Share a public IP address' in the Internet settings).
In this way it is the only device that the cable modem talks to.

Without this (if you have it set to Bridge mode) it lets each internal computer talk directly to the cable modem, but cable modems are dumb and will only talk to one device at at time - therefore if the first machine it saw was the iMac, then the iMac is the only machine it will talk to until it's power cycled (then the lock is released and another machine can talk).

I believe that is what you meant and it was already selected like that. I don't see "bridge mode". I see this --> which is not selected: "share a range of IP addresses using only DHCP"??

I'm still having the same issue which is frustrating. When we want to use multiple computers, we have to turn the cable modem on/off and wait for it to connect again. Otherwise we give up and just hard wire connect the one imac.

thanks for trying to help me. any other ideas? or am I doing something wrong.